14 research outputs found
Free -distributive lattice over an -element chain
In this note we provide an explicit construction of , the free -distributive lattice over an -element chain, different from those given by Cignoli [4] and Abad--DÃaz Varela [1], and prove that can be endowed with a structure of a De Morgan algebra.Fil: Monteiro, Luis. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Matemática BahÃa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahÃa Blanca; ArgentinaFil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Zander, Marta Amalia. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentin
Topological representation for monadic implication algebras
In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Cimadamore, Cecilia Rossana. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Matemática BahÃa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahÃa Blanca; ArgentinaFil: DÃaz Varela, José Patricio. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Matemática BahÃa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahÃa Blanca; Argentin
Independence-friendly cylindric set algebras
Independence-friendly logic is a conservative extension of first-order logic
that has the same expressive power as existential second-order logic. In her
Ph.D. thesis, Dechesne introduces a variant of independence-friendly logic
called IFG logic. We attempt to algebraize IFG logic in the same way that
Boolean algebra is the algebra of propositional logic and cylindric algebra is
the algebra of first-order logic.
We define independence-friendly cylindric set algebras and prove two main
results. First, every independence-friendly cylindric set algebra over a
structure has an underlying Kleene algebra. Moreover, the class of such
underlying Kleene algebras generates the variety of all Kleene algebras. Hence
the equational theory of the class of Kleene algebras that underly an
independence-friendly cylindric set algebra is finitely axiomatizable. Second,
every one-dimensional independence-friendly cylindric set algebra over a
structure has an underlying monadic Kleene algebra. However, the class of such
underlying monadic Kleene algebras does not generate the variety of all monadic
Kleene algebras. Finally, we offer a conjecture about which subvariety of
monadic Kleene algebras the class of such monadic Kleene algebras does
generate.Comment: 42 pages. Submitted to the Logic Journal of the IGPL. See also
http://math.colgate.edu/~amann